Large-chiral-number corner modes in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mrow><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow></mml:math>-class higher-order topolectrical circuits

Abstract

Topological corner states are exotic topological boundary states bounded to zero-dimensional geometry even when the dimension of bulk systems is larger than one. So far, all previous realizations of higher-order topological insulators (HOTI) phases are hallmarked by ${\mathbb{Z}}_{2}$ topological invariants and therefore have only one corner state at each corner. Here, we report an experimental demonstration of $\mathbb{Z}$-class HOTI phases in electrical circuits, characterized by multipole chiral numbers $N$, hosting large-number corner modes at each corner. By measuring the impedance spectra and distributions, we clearly observe that the multipole corner modes in $\mathbb{Z}$-class HOTI phases feature scalable mode areas. Moreover, we find that the local density of states (LDOS) at each corner is maximally distributed at $N$ corner unit cells, differing conspicuously from the ${\mathbb{Z}}_{2}$-class case, where the LDOS only dominates over one corner unit cell, allowing us to probe the topological number $N$ and reveal the corresponding fractional corner charges. Our results extend the observation of HOTIs from the ${\mathbb{Z}}_{2}$ class to the $\mathbb{Z}$ class and the coexistence of spatially overlapping large numbers of corner modes that may enable exotic topological devices that require high-degeneracy boundary states.